Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
A Logical Framework for Graded Predicates Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

Doing Without Nature

verfasst von : Frederik Van De Putte, Allard Tamminga, Hein Duijf

Erschienen in: Logic, Rationality, and Interaction

Verlag: Springer Berlin Heidelberg

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We show that every indeterministic n-agent choice model \(M^i\) can be transformed into a deterministic n-agent choice model \(M^d\), such that \(M^i\) is a bounded morphic image of \(M^d\). This generalizes an earlier result from Van Benthem and Pacuit [16] about finite two-player choice models. It further strengthens the link between STIT logic and game theory, because deterministic choice models correspond in a straightforward way to normal game forms, and choice models are generally used to interpret STIT logic.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel The Dynamics of Group Polarization
Nächstes Kapitel Axiomatizing Epistemic Logic of Friendship via Tree Sequent Calculus
Fußnoten
1
See e.g. [12] for a solid introduction to the theory of strategic games.
 
2
This notion is usually referred to as “\(\alpha \)-effectivity” in game theory. We provide a formal definition of it in Sect. 2.
 
3
In the two-agent case, cells correspond to the “innermost squares” in the matrix. See Sect. 2 for the general definition of cells in a choice model.
 
4
The notion of effectivity is monotonic: whenever an agent is effective for X, it is also effective for every superset of X. In the current example, this means that agent 1 is e.g. also effective for \(\{a,b,c,d\}\).
 
5
[G] is also known as the Chellas STIT, after the seminal work in the logic of agency by Chellas [4].
 
6
Given our semantics, \(\square \varphi \) is definable as \([i][j]\varphi \) for \(i\ne j\). We will however treat \(\square \) as primitive for reasons of clarity.
 
7
This property may be called the intersection property. In Sect. 6 we briefly mention how it relates to some completeness results.
 
8
In [13, 14], the authors actually establish a correspondence between strategic games and choice models enriched with preference relations \(\preceq _i\) for the agents \(i\in N\). Ignoring this extra dimension, one obtains exactly the correspondence that we spell out in the present section.
 
9
See e.g. [2] for an introduction to the notion of bounded morphisms in modal logic.
 
10
For the grand coalition N, determinism obviously makes a difference. That is, within the class of all choice frames, determinism is characterized by the axiom \([N]\varphi \leftrightarrow \varphi \), which is not valid on indeterministic choice frames.
 
11
See e.g. [7] for an introduction to modal product logics.
 
12
Where \(i,j\in \mathbb {N}\), \({i} \mathsf{mod} {j}\) is shorthand for “i modulo j”, i.e., the remainder after division of i by j.
 
13
Note that we apply the \(\mathsf{card}\) function both to finite and infinite (even uncountable) sets.
 
14
Since \(X\subseteq W^i\), it can be easily verified that there is at least one such function \(g^X\).
 
Literatur
1.
Belnap, N., Perloff, M., Xu, M., Bartha, P.: Facing the Future: Agents and Choice in Our Indeterminist World. Oxford University Press, Oxford (2001)
2.
Blackburn, P., De Rijke, M., Venema, Y.: Modal Logic. Cambridge Tracts in Theoretical Computer Science (2001)
3.
Broersen, J., Herzig, A., Troquard, N.: A normal simulation of coalition logic and an epistemic extension. In Samet, D. (ed.) Proceedings of the 11th Conference on Theoretical Aspects of Rationality and Knowledge, pp. 92–101. ACM (2007)
4.
5.
Ciuni, R., Horty, J.: Stit logics, games, knowledge, and freedom. In: Baltag, A., Smets, S. (eds.) Johan van Benthem on Logic and Information Dynamics. OCL, vol. 5, pp. 631–656. Springer, Cham (2014). doi:10.​1007/​978-3-319-06025-5_​23
6.
Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning About Knowledge. MIT Press, Cambridge (2003)MATH
7.
Gabbay, D., Kurucz, A., Wolter, F., Zakharyaschev, M.: Many-dimensional Modal Logics: Theory and Applications. Studies in Logic and the Foundations of Mathematics, vol. 148. North Holland Publishing Company (2003)
8.
Herzig, A., Schwarzentruber, F.: Properties of logics of individual and group agency. In: Areces, C., Gobldblatt, R. (eds.) Advances in Modal Logic. College Publications (2008)
9.
10.
11.
Lorini, E., Schwarzentruber, F.: A logic for reasoning about counterfactual emotions. Artif. Intell. 175(3), 814–847 (2011)MathSciNetCrossRefMATH
12.
Osborne, M., Rubinstein, A.: A Course in Game Theory, 7th edn. MIT Press, Cambridge (2001)MATH
13.
14.
15.
van Benthem, J.: Logic in Games. MIT Press, Cambridge (2014)MATH
16.
17.
Metadaten
Titel
Doing Without Nature
verfasst von
Frederik Van De Putte
Allard Tamminga
Hein Duijf
Copyright-Jahr
2017
Verlag
Springer Berlin Heidelberg
Buch
Logic, Rationality, and Interaction

Print ISBN: 978-3-662-55664-1

Electronic ISBN: 978-3-662-55665-8

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-662-55665-8_15